Some will argue the source of the Acts 15 laws is Leviticus, like the OP. Others will argue they source to the Noahide Laws in Genesis 15. Others will argue they source to the Book of Jubilees. Others will argue they were created about the time we hear of them in Acts 15.
The reason it can't be Leviticus is because of the cherry-picking. Moses is read in the synagogue, why just four laws, why not the 10 commandments? Why not find them in Genesis 15? Like the Book of Jubilees, there are some similarities, but not the number of only four. Thus, we are left with the idea that the Jerusalem Council created them.
So, to directly answer the OP question, were the four prohibitions "based on" Leviticus, not really. There is no proof. The Jerusalem Council may have picked the most offensive laws, but it appears the restrictions source solely and directly to those in the Council.
To take a closer look at the reasoning, we know the Jerusalem Council was about the question of how one is saved. It was not about "being clean" or "entering the place of worship".
And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved. Acts 15:1
By the time they assemble in Jerusalem, the answer was expanded to include circumcision and observing the whole of the Mosaic Law.
But there rose up certain of the sect of the Pharisees which believed, saying, That it was needful to circumcise them, and to command them to keep the law of Moses. Acts 15:5
The discussion no doubt was lively and loud. Peter stands and speaks finally into the respectful silence.
And [God] put no difference between us [Israelites] and them [Gentiles], purifying their hearts by faith. Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear? Acts 15:9-10
Peter tells the truth. No one can 100% follow the Mosaic Law. Yet, the Law says that if you follow every command, you will be righteous.
And it shall be our righteousness, if we observe to do all these commandments before the LORD our God, as he hath commanded us. Deut 6:25
But again, no one succeeds, hence the sacrificial laws must be perfectly followed also. Peter and the others understand. Peter provides the way out of condemnation.
But we [Israelites] believe that through the grace of the Lord Jesus Christ we shall be saved, even as they [Gentiles]. Acts 15:11
So, the question of how to be saved, declared righteous, has been answered. Yet, not all can quite believe. James, the Lord's brother, takes over.
Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
Wow. James puts the yoke back on the Israelites. But for Gentiles, it's a lighter yoke, there are only four laws needed to make one righteous.
But that we write unto them, that they abstain from pollutions of idols, and from fornication, and from things strangled, and from blood. Acts 15:20
There they are. What's the source? They claim themselves and the Holy Spirit.
For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things; Acts 15:28
Why four? We don't know, but Moses is important.
For Moses of old time hath in every city them that preach him, being read in the synagogues every sabbath day.
Rabbis preach Moses' way of righteousness in every synagogue every Sabbath. You get a feeling that if they can do 613 laws, certainly you can do 4.
So, they draft a letter and send the disciples with the message.
That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well. Acts 15:29
In short, Acts 15 was about the question how to be saved (righteous before God). They answer the question; that is, saved by grace apart from works. The only reason to observe the four laws is to respect the Rabbis who preach Moses. They would add nothing to salvation by grace through faith in Jesus Christ.